1. Study of the Isovector Spin Monopole Resonance via the (t, 3 He) Reactions at 300MeV/u Kenjiro Miki (RCNP)

2. University of Tokyo K. M. (  Now in RCNP) Hideyuki SAKAI Kentaro YAKO Shumpei NOJI University of Tokyo K. M. (  Now in RCNP) Hideyuki SAKAI Kentaro YAKO Shumpei NOJI RIKEN Nishina Center Masaki SASANO Hidetada BABA Tetsuya OHNISHI Hiroyuki TAKEDA Naoki FUKUDA Daisuke KAMEDA Yoshiyuki YANAGISAWA Toshiyuki KUBO RIKEN Nishina Center Masaki SASANO Hidetada BABA Tetsuya OHNISHI Hiroyuki TAKEDA Naoki FUKUDA Daisuke KAMEDA Yoshiyuki YANAGISAWA Toshiyuki KUBO CNS, Univ. of Tokyo Tomohiro UESAKA Susumu SHIMOURA Shin'ichiro MICHIMASA Shinsuke OTA Akito SAITO Yoshiko SASAMOTO Hiroyuki MIYA Hiroshi TOKIEDA Shoichiro KAWASE CNS, Univ. of Tokyo Tomohiro UESAKA Susumu SHIMOURA Shin'ichiro MICHIMASA Shinsuke OTA Akito SAITO Yoshiko SASAMOTO Hiroyuki MIYA Hiroshi TOKIEDA Shoichiro KAWASE Michigan State Univ. Remco G.T. ZEGERS Michigan State Univ. Remco G.T. ZEGERS Collaborators Univ. of Notre Dame Georg P.A. BERG Univ. of Notre Dame Georg P.A. BERG Kyoto University Takahiro KAWABATA Kyoto University Takahiro KAWABATA University of Aizu Hiroyuki SAGAWA University of Aizu Hiroyuki SAGAWA Sichuan University Chunlin BAI Sichuan University Chunlin BAI

3. 1. Introduction

4. Giant resonances Giant resonance – Collective motion of nuclei – Exhaust major part of sum-rule strength (e.g. >50%) – Related to bulk property of nuclei – Grouped by quantum number changes  L,  S and  T d d p,np,n p n p n p n p,np,n p n IVSMR ISGMR IVGMRISSMR IVGDR IVGQR ISGQRISSQR ISSDR  L=0  L=1  L=2  S=0  S=1 p n p n IVSDR IVSQR (monopole) (dipole) (quadrupole) isoscalar  T=0 isovector  T=1 isovector spin monopole resonance (IVSMR)

5. Shed light on the role of the spin-isospin degrees of freedom in nuclear matter  unexplored region Test of the microscopic description of the nuclear structure  the effective N-N interaction in nuclei, especially the  channel Model independent sum-rule (future)  Neutron skin thickness  Selection of EoS of neutron matter Significance Isovector Spin Monopole Resonance the isovector spin monopole resonance (IVSMR)  L=0,  S=1,  T=1,  n=1 ( 2 ℏ  Status of experimental study - Some signatures have been reported. - But none of them clearly identify IVSMR. Data are scarce especially for IVSMR(  + ). Status of experimental study - Some signatures have been reported. - But none of them clearly identify IVSMR. Data are scarce especially for IVSMR(  + ). IVSM operator : Quantum number : p n n p hole particle IVSMR(  + )  =+1 transfer

6. IVSMR – Isovector (  T=1) – Spin-flip (  S=1) – Monopole (  L=0) – 2 ℏ  excitation (  n=1) Identification of the IVSMR Comparison between: (t, 3 He) reaction and (n,p) reaction at the intermediate energy

7. IVSMR – Isovector (  T=1) – Spin-flip (  S=1) – Monopole (  L=0) – 2 ℏ  excitation (  n=1) Isovector (  T=1) (t, 3 He),(n,p) …charge-exchange Spin-flip (  S=1) Incident energy dependence of   S=1 /   S=0 Identification of  T=1 and  S=1 W.G.Love, M.A.Franey : PRC 24 (1981) 1073 Selectively excite spin-flip modes. Selectively excite  + modes IVSMR can be dominant in the  + direction, because most of GT,(SDR) are Pauli-blocked. (+SQR)

8. IVSMR – Isovector (  T=1) – Spin-flip (  S=1) – Monopole (  L=0) – 2 ℏ  excitation (  n=1) Identification of  L=0 Multipole decomposition analysis (MDA) Angular distribution  characteristic dependence on  L  exp is decomposed into each  L component by fitting the calculated cross section.  L=2  L=1  L=0 Forward peaking  L=0 component can be precisely extracted because it has a unique forward-peaking nature.  L=0 component can be precisely extracted because it has a unique forward-peaking nature.

9. IVSMR – Isovector (  T=1) – Spin-flip (  S=1) – Monopole (  L=0) – 2 ℏ  excitation (  n=1) Identification of  n=1 Separation of GT(  n=0 ) and IVSM (  n=1) (t, 3 He) -- IVSMR (large) + GT (n,p) -- IVSMR (small) + GT Different sensitivity on IVSMR  absorption effect 3 He & t (  ~large) 1.5 fm(absorptive) p & n (  ~small) 5 fm(transparent) The transition density of IVSMR has a radial node. Cross section Owing to the different sensitivity, IVSM can be distinguished from GT. Owing to the different sensitivity, IVSM can be distinguished from GT. IVSMR should appear as a difference. MeanFreePath Radius r (fm)

10. IVSMR (  - ) ? ? absorptive transparent Previous Experiment 90 Zr( 3 He,t).vs. 90 Zr(p,n) Enhancement for ( 3 He,t)  Signature of IVSMR Similar structure also for 54 Fe, 208 Pb Good example of absorption effect But, other excitations can also be enhanced.   L=0 must be extracted via the multipole decomposition analysis. Transparent Absorptive ( 3 He,t) (p,n)(p,n) Need to compare the extracted  L=0 components IVSMR (  + ) ? 208 Pb(n,p) 458MeV.vs. 198MeV -- low statistical accuracy -- insufficient absorption effect -- low statistical accuracy -- insufficient absorption effect A bump at 15MeV, but not uniquely identified as the IVSMR. Brockstedt et. al. NPA530(1991)571 Moinester et. al. PLB230(1989)41 Other pioneering works: Guillot et. al., PRC73(2006)014616  KVI Guess et. al., PRC83(2011)064318  NSCL Not exclusively identify the IVSMR(  + )

11. Purpose : Identify the IVSMR (  + ) exclusively Experiment : 208 Pb, 90 Zr(t, 3 He) reaction @ 300MeV/u – Performed at RI Beam Factory (RIBF) at RIKEN Triton at 300MeV/u  Feasible only at RIBF – Double-differential cross section spectra were measured at 0 < Ex < 40MeV and at 0 <  < 4deg. Analysis/Discussion : –  L=0 component was extracted via the multipole decomposition analysis. – Through the comparison with the previous (n,p) spectra, the IVSMR is exclusively identified. This experiment Comparison between: (t, 3 He) reaction and (n,p) reaction at the intermediate energy Already measured at RCNP and TRIUMF This work (at 300MeV/u)

12. 2. Experiment

13. RI Beam Factory (RIKEN) Experiment 4 He 2+ 320MeV/u 300pnA 3 H + 300MeV/u Production Target 9 Be 4cm Beam tuning, Calibration of Ion Optics PPAC, MWDC, Plastic 3 He 2+ Momentum Slit Achromatic transport CRDC, Plastic Angular Collimator Purity > 99% 10 7 pps Secondary Target 208 Pb, 90 Zr,CH 2 |  F2 |<15mrad |  p/p| = 1/2600 (0.6MeV)

14. Beam Primary : 4 He 320MeV/u 300pnA Secondary : triton 300MeV/u 1x10 7 pps Purity > 99% Measured Spectra 208 Pb(t, 3 He) 208 Tl 90 Zr (t, 3 He) 90 Y CH 2 (t, 3 He) Resolution (FWHM)  E = 2.5MeV - Spread of secondary beam – 1.8MeV - Energy loss in target – 1.6MeV  = 0.5deg - Spread of secondary beam – 8mrad - Multiple scattering in target – 5mrad Error bars Statistical accuracy – 3% (for 0.15msr ・ 1MeV –bin) Systematic accuracy – 7% Experimental Conditions 0 ≲ E x ≲ 40MeV 0 ≲  ≲ 4° @

15. 3. Results/Discussion

16. Measured double-differential cross section 208 Pb(t, 3 He) 90 Zr(t, 3 He)

17. Angular distribution calc. – DWBA (FOLD) – 1p1h configuration 208 Pb -- (particle) sdgi shell : (hole) sdg shell 90 Zr -- (particle) sdg, pfh shell : (hole) sd, pf shell – Single particle wave function Woods-Saxon Potential – N-N interaction Franey-Love effective t-matrix 325 MeV – Optical Potential Double folding of CEG07b (G-Matrix interaction) χ 2 fitting Multipole Decomposition Analysis (MDA) DWBA calculation χ 2 fitting to the experimental angular distribution  Determine each  L component χ 2 fitting to the experimental angular distribution  Determine each  L component Δ J π = 1 + (ΔL=0) 0 -,1 -,2 - (ΔL=1) 3 + (ΔL=2) 4 - (ΔL=3) 5 + (ΔL=4)

18. Results of MDA 208 Pb(t, 3 He) 90 Zr(t, 3 He)

19. Results of MDA 208 Pb(t, 3 He) 90 Zr(t, 3 He) Red region corresponds to  L=0,  S=1,  T=1 Still need to extract  n=1 Red region corresponds to  L=0,  S=1,  T=1 Still need to extract  n=1

20.  n=1 : Comparison between (t, 3 He) and (n,p) Identification of the IVSMR (t, 3 He)  L=0 = GT + IVSMR(Large) (n,p)  L=0 = GT + IVSMR(Small)

21.  n=1 : Comparison between (t, 3 He) and (n,p) Identification of the IVSMR Reanalyze previous (n,p) data by FOLD-MDA [ The same condition as (t, 3 He) analysis] Raywood et.al. (TRIUMF) NPA 625(1997)675 Yako et.al. (RCNP) PLB 615(2005)193 (t, 3 He)  L=0 = GT + IVSMR(Large) (n,p)  L=0 = GT + IVSMR(Small)

22.  n=1 : Comparison between (t, 3 He) and (n,p) Identification of the IVSMR (t, 3 He)  L=0 = GT + IVSMR(Large) (n,p)  L=0 = GT + IVSMR(Small) 208 Pb1.57 90 Zr1.83 NPA530(1991)571 Normalize GT component Reanalyze previous (n,p) data by FOLD-MDA [ The same condition as (t, 3 He) analysis] Raywood et.al. (TRIUMF) NPA 625(1997)675 Yako et.al. (RCNP) PLB 615(2005)193

23.  n=1 : Comparison between (t, 3 He) and (n,p) Identification of the IVSMR Large enhancement for (t, 3 He)  Clearest identification of the IVSMR(  + ) (RCNP data) (TRIUMF data) (t, 3 He).vs. (n,p) (t, 3 He)  L=0 = GT + IVSMR(Large) (n,p)  L=0 = GT + IVSMR(Small) 208 Pb1.57 90 Zr1.83 NPA530(1991)571 Normalize GT component

24. Comparison with Theory (HF-QRPA+DWBA) Theory – DWBA calc. by the program FOLD – Target wave function (J  =1 + states) self-consistent HF-RPA : Bai, Sagawa et. al. – Effective interactions : SGII+Te3 and T43 SGII+Te3 Shows concentration of the cross section in a narrow region. Does not reproduce the exp. Data. T43 Reproduce the overall distribution well. Exp. (mb/sr) Theo.(T43) (mb/sr) Exp./Theo. (%) 208 Pb48 ± 531160 90 Zr77 ± 851151 Further theoretical study is now in progress. (C.L.Bai, H.Sagawa and K.Miki) T43 provides a good description.  integ.

25. Systematics of  L=0 cross section Average energy of  L=0 cross section ─ T43 calc. well reproduces our results. ─ Fitting with A -1/3 dependence  E x = 97A -1/3 Implying the repulsive nature of the spin-isospin channel Larger than typical value : 2 ℏ  = 80A -1/3 

26. Comment on Tensor ? Large amount of GT? Red  IVSM Orange  contains GT (RCNP data) (TRIUMF data) Exp : 10%  Theo. : ~0%

27. i.The isovector spin monopole resonance (IVSMR) is very important. It is closely related to the fundamental property of nuclei. ii.The double-differential cross sections for the 208 Pb, 90 Zr(t, 3 He) reactions at 300MeV were measured at 0 ≦ E x ≦ 40 MeV and 0 ≦  ≦ 4 deg. iii.The MDA was applied to both of our (t, 3 He) and previous (n,p) spectra, and the  L=0 components were extracted. From their comparison, the IVSMR was distinguished from GT. This results provide the clearest identification of the IVSMR(  + ). iv.The measured  L=0 cross section was well reproduced by the HF-QRPA+DWBA calculation with the effective interaction T43. v.The average energy of  L=0 cross section at 0deg was given by 97A -1/3. Represents the repulsive nature of the spin-isospin channel. Conclusion

28. supplimentary

29. GT Cross Section We have been seriously concerned about the large amount of GT cross sections 21.02 mb/sr13.27 mb/sr Unit cross section 1.91*1.57 = 3.0 mb/sr 3.4*1.83 = 6.2 mb/sr B(GT)7.02.1 w/o with T21 0.37 0.649 T32 0.49 0.66 T43 0.655 0.671 T54 0.78 0.71 SGII+Te1 0.798 0.84 SGII+Te2 0.798 0.721 SGII+Te3 0.798 0.748 Theory (Bai-san,Sagawa-san) Tensor w/o with T21 0.439 0.443 T32 0.471 0.463 T43 0.495 0.485 T54 0.53 0.507 SGII+Te1 0.488 0.506 SGII+Te2 0.488 0.479 SGII+Te3 0.488 0.484 Tensor wo F(q,  )

30. Systematics of  L=0 cross section Average energy of  L=0 cross section ─ Add Coulomb energy difference E coul = Ex(IAS) ─ Fitting with A -1/3 dependence  E x = 169A -1/3 (But needs additional terms.) Still Larger than typical value : 2 ℏ  = 80A -1/3 Cf. isovector monopole (T=1, Tz=0) E x = 170A -1/3